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Research articles

ScienceAsia 49 (2023):ID 838-845 |doi: 10.2306/scienceasia1513-1874.2023.052


A complementary Hyers-Ulam stability of alternative equation of Jensen type


Teerapol Sukhonwimolmal

 
ABSTRACT:     We studied the stability of the alternative functional equation ?f (x ? y) ? 2f (x) + f (x + y)? ? f (x ? y) + f (x + y)? = 0 (*) for all x, y ? G, where f : G ? B is a function from commutative group G to a real Banach space B, and found that if ?f (x ? y) ? 2f (x) + f (x + y)? ? ? or ?f (x ? y) + f (x + y)? ? ? for each x, y ? G, then there exists a solution f ? : G ? B of (*) such that ?f (x) ? f ? (x)? ? 12?. The general solution of (*) was also achieved.

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a Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002 Thailand

* Corresponding author, E-mail: teerasu@kku.ac.th

Received 19 Oct 2022, Accepted 4 Jun 2023